Dirichlet's Theorem on Primes in Arithmetic Progressions

Key Points

• The aim is to prove that any arithmetic progression defined by integers a and d, where gcd(a,d)=1, contains infinitely many prime numbers.
• Formulated a proof utilizing properties of arithmetic progressions and number theory principles.
• Analyzed the relationship between a, d, and the distribution of prime numbers.
• Employed logical reasoning based on existing mathematical frameworks.
• Demonstrated the existence of infinitely many primes in specified arithmetic progressions.
• Confirmed gcd conditions crucial for establishing the infinite nature of primes in the sequences.